The Infinitum company's value of outstanding equity is USD 400 million, and you have estimated its beta to be 1.2. Infinitum has four-year zero-coupon debt outstanding with a face value of USD 100 million that currently trades for USD 80 million. The firm pays no dividends and reinvests all of its earnings. The risk-free rate of interest is currently 4.00% and is continuously compounded, while the standard deviation of the return on firm's assets is equal to 0.6. From the standard normal distribution table, please use the 4-digit value. Using the Black-Scholes formula, the estimated unlevered beta of the firm is closest to:

Question

BlackTom AI · Accepted Answer

We begin by identifying the key inputs: the levered beta given for the firm is 1.2, and the market values provided are equity 400 million and debt 80 million (market value of debt). First, determine the debt-to-equity ratio that feeds the beta unlevering formula.

D/E = 80 / 400 = 0.20.

Under the classic Hamada/Modigliani-Miller framework (with taxes ignored or t ≈ 0 for this unlevering step), the relation between levered beta (βL) and unlevered beta (βU) is:
βL = βU × [1 + (1 − t) × (D/E)]. If we assume taxes are negligible (t ≈ 0), this simplifies to:
βL = βU × [1 + D/E] = βU × (1 + 0.20) = βU × 1.20.
Thus,
beta_unlevered = beta_levered / 1.20 = 1.2 / 1.20 = 1.0.

Now compare this computed unlevered beta to the available answer choices. The exact calculation yields 1.0, which is closest to 1.02 among the options.

Why the other options are not correct:
- A. 1.80: This would require a much larger unlevered beta, implying a far higher asset risk than implied by the given levered beta and debt level; it does not fit the standard levered/unlevered relationship with D/E = 0.20.
- C. 1.41: Similar issue as A; this would indicate substantially more asset risk than what the levered beta and modest debt load imply under the usual formula.
- D. 0.20: This is far too small for an unlevered beta given an equity beta of 1.2; it would suggest extremely low asset risk, inconsistent with the provided levered beta.

So, applying the conventional unlevering formula with a small debt ratio yields an unlevered beta of about 1.0, which is closest to 1.02.

View Explanation

Log in for full answers

Similar Questions

What will the firm's equity beta be if it gets rid of all its debts?

Based on the brief reading, you should be able to understand that if you start with a company's levered beta and convert it to an unlevered beta, then you are...

The equations given for levered and unlevered betas are not so tough, once you have all the right information. For example, say you have a levered beta of 1.5 for a company's stock, and that company has a debt-to-equity ratio of 0.25. The relevant tax rate is 21.0%. What is the unlevered beta?

Unlevered beta is often called...

You can transform a levered beta into an unlevered beta by...

Your company continuously adjusts its leverage to maintain a target D/V ratio of 50%. Its equity beta is 1.4, and its debt beta is 0.2. What would the company’s equity beta be if it did not have leverage?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler